Question 1

Determine the number of solutions of the equation 5x $4$ - 3x $2$ = 10x $5$ - 20x $6$ $+$ 63x $+$ 5.

Accepted Answer

A) 0 
B) 1 
C) 2 
D) 3 
E) 4
F)5
G)6
H)7

Question 2

The following time-of-day and temperature (FS1U1P1$\circ$S1S1P0) were gathered during a gorgeous midsummer day in Fargo, North Dakota:
$$\begin{array} { | c | c | } 
\hline \text { Time of Day } & \text { Temperature } \
\hline 18 & 74 \
\hline 17 & 73 \
\hline 16 & 73 \
\hline 15 & 72 \
\hline 14 & 70 \
\hline 13 & 70 \
\hline 12 & 68 \
\hline 11 & 66 \
\hline 10 & 63 \
\hline 9 & 62 \
\hline 8 & 59 \
\hline 7 & 58 \
\hline
\end{array}$$
Source: National Weather Service; www.weather.gov
(a) Make a scatter plot of these data.
(b) Fit a linear model to the data.
(c) Fit an exponential model to the data.
(d) Fit a quadratic model to the data.(e) Use your equations to make a table showing the predicted temperature for each model, rounded to the nearest degree.
(f) The actual temperature at 8:00 p.m. (20 hours) was 70° F. Which model was closest? Which model was second-closest?
(g) All of the models give values that are too high for each of the times after 6:00 PM. What is one possible explanation for this?

Accepted Answer

The answer of The following time-of-day and temperature (FS1U1P1$\circ$S1S1P0) were...

Question 3

Find the domain of the inverse for f (x) = $\sqrt { 2 x - 5 }$ .

Accepted Answer

A) ( $- \infty , - \frac { 5 } { 2 }$ ] 
B) ( $- \infty$ , 0] 
C)  $\left[ - \frac { 5 } { 2 } , \frac { 5 } { 2 } \right]$ 
D)  $\left( - \infty , \frac { 5 } { 2 } \right]$ 
E)  $\left[ - \frac { 5 } { 2 } , \infty \right)$ 
F)[0, $\infty$ )

G) $\left[ \frac { 2 } { 5 } , \infty \right)$ 
H) $\left[ \frac { 5 } { 2 } , \infty \right)$

Question 4

Find functions f and g such that F(x) = 1 $\sqrt { 1 - \cos ^ { 2 } x }$ = $( f \circ g ) ( x )$

Accepted Answer

The answer of Find functions f and g such that...

Question 5

Which of the following are graphs of functions?

Accepted Answer

A) I only 
B) II only 
C) III only 
D) I and II only 
E) I and III only
F)I, II, and IV only
G)II and V only
H)I,II, III only

Question 6

Make a rough sketch of the graph of y = (1.1) $- x$ . Do not use a calculator.

Accepted Answer

The answer of Make a rough sketch of the graph...

Question 7

Relative to the graph of y = sin x, where x is in the radians, the graph of y = sin x, where x is in degrees, is changed in what way?

Accepted Answer

A) Compressed horizontally by a factor of $\frac { 180 } { \pi }$ 
B) Stretched vertically by a factor of $\frac { 180 } { \pi }$ 
C) Compressed horizontally by a factor of $\frac { 90 } { \pi }$ 
D) Stretched horizontally by a factor of $\frac { 90 } { \pi }$ 
E) Compressed vertically by a factor of $\frac { 90 } { \pi }$ 
F)Stretched vertically by a factor of $\frac { 90 } { \pi }$ 
G)Stretched horizontally by a factor of $\frac { 180 } { \pi }$ 
H)Compressed vertically by a factor of $\frac { 180 } { \pi }$

Question 8

Make a rough sketch of the graph of y = 3 (4 - 2 $x$ ). Do not use a calculator.

Accepted Answer

The answer of Make a rough sketch of the graph...

Question 9

Solve the equation $\log _ { 9 }$ (ln $x ^ { 3 }$ ) = 1

Accepted Answer

A)  $x = 3 ^ { e }$ 
B)  $x = 3 e$ 
C)  $x = e / 3$ 
D)  $x = 1$ 
E)  $x = e ^ { 2 }$ 
F) $x = 1 / e$ 
G) $x = 3 / e$ 
H) $x = e ^ { 3 }$

Question 10

Let f (x) = $\sqrt { 16 - x ^ { 2 } }$ . Find each of the following:
(a) f (0) $+$ f ( $- 2$ )
(b) f (x $+$ 2)
(c) [f (x)] $2$ (d) f (x $2$ )

Accepted Answer

The answer of Let f (x) = \(\sqrt { 16...

Question 11

Find the smallest value in the domain of the function f (x) = $\sqrt { 2 x - 5 }$ .

Accepted Answer

A) 2 
B)  $\frac { 5 } { 2 }$ 
C) 5 
D)  $\frac { 2 } { 5 }$ 
E) -2
F)1
G)0

H)-5

Question 12

Consider the data below:
$$\begin{array} { | c | c | c | c | c | c | c | } 
\hline t & 1 & 2 & 3 & 4 & 5 & 6 \
\hline y & 2.4 & 19 & 64 & 152 & 295 & 510 \
\hline
\end{array}$$
(a) Fit both an exponential curve and a third-degree polynomial to the data.(b) Which of the models appears to be a better fit? Defend your choice.

Accepted Answer

The answer of Consider the data below:
\[\begin{array} { | c...

Question 13

Find the range of the function $f ( x ) = \left\{ \begin{array} { l l } 
x ^ { 2 } - 4 x & \text { if } x \leq 2 \
| x - 4 | & \text { if } x > 2
\end{array} \right.$ .

Accepted Answer

A) [0,$\infty$). 
B) (-$\infty$,2] 
C) [-4, $\infty$). 
D) (-$\infty$, 0] 
E) [4, $\infty$)
F)(-$\infty$,4]
G)[2, $\infty$)
H)(-$\infty$,4] .

Question 14

A tank used for portland cement consists of a cylinder mounted on top of a cone, with its vertex pointing downward. The cylinder is 30 feet high, both the cylinder and the cone have radii of 4 feet, and the cone is 6 feet high.  (a) Determine the volume of cement contained in the tank as a function of the depth d of the cement.(b) What is the domain of the function?

Accepted Answer

The answer of A tank used for portland cement consists...

Question 15

Decide whether the given function has an inverse. Defend your decision.

(a)  P (x) is the cost, in cents, of mailing a letter that weighs x ounces.

(b)  C (t) is the total number of cars which have driven past a particular point along a highway during a specific day where t represents the time, in hours, since midnight.

(c)  F (d) is the amount of fuel, in gallons, in your car when you have traveled d miles on a particular tankful of gas.

(d)  S (t) is the number of shoppers entering the Mall of America where t is the number of minutes past midnight on one particular day.

(e)  T (t) is the temperature inside an oven where t is the time, in minutes, from the beginning to the end of the oven's self-cleaning cycle.

(f)  V (x) is the volume of a cube whose side has length x.

(g)  f (n) is the number of students enrolled in your calculus class on the nth day of the term.

Accepted Answer

The answer of Decide whether the given function has an...

Question 16

Find the range of the inverse for f (x) = $- \frac { 3 } { 5 + 2 x }$ .

Accepted Answer

A)  $\left( - \infty , - \frac { 5 } { 2 } \right)$ 
B) ( $- \infty$ , 0) 
C)  $\left( - \frac { 5 } { 2 } , \frac { 5 } { 2 } \right)$ 
D)  $\left( - \infty , \frac { 5 } { 2 } \right)$ $\cup$ $\left( \frac { 5 } { 2 } \infty \right)$ 
E)  $\left( - \frac { 5 } { 2 } , \infty \right)$ 
F)(0, $\infty$ )

G) $\left( \frac { 5 } { 2 } , \infty \right)$ 
H) $\left( - \infty , - \frac { 5 } { 2 } \right)$ $\cup$ $\left( - \frac { 5 } { 2 } \infty \right)$

Question 17

The position after t seconds of a projectile red with initial velocity v0 (measured in ft/s) at an angle above the horizontal from an initial height of h0 (measured in ft) is given by the parametric equations $x = \left( v _ { 0 } \cos \alpha \right) t$ $y = \left( v _ { 0 } \sin \alpha \right) t - 16 t ^ { 2 } + h _ { 0 }$ .
(a) Eliminate the parameter t to show that the trajectory of the projectile is a parabola.
(b) If the projectile is red with an initial velocity of 300 ft/s from a height of 5 ft, what should be the angle of elevation in order to hit a target at the same height as the initial height, 900 ft downrange?
(c) If the projectile is red with an angle of elevation of 40S1U1P1$\circ$S1S1P0 and it strikes a target at the same height as the initial height, 600 ft downrange, what was the initial velocity of the projectile?

Accepted Answer

The answer of The position after t seconds of a...

Question 18

Find the value of log $2$ $\frac { 1 } { 8 }$ .

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 3 }$ 
C) 0 
D) 1 
E)  - 1
F)2
G) - 2
H) - 3

Question 19

Find the inverse function for f (x) = $\frac { x - 1 } { x + 1 }$ .

Accepted Answer

A)  $\frac { x + 1 } { x - 1 }$ 
B)  $\frac { x } { x + 1 }$ 
C)  $\frac { x + 1 } { x }$ 
D)  $\frac { 1 + x } { 1 - x }$ 
E)  $\frac { x + 1 } { 1 - x }$ 
F) $\frac { x } { x - 1 }$ 
G) $\frac { x - 1 } { x + 1 }$ 
H) $\frac { x - 1 } { x }$

Question 20

A function has a domain [-4, 4] and a portion of its graph is shown.  (a) Complete the graph of f of its is known that f is an even function.(b) Complete the graph of f if it is known that f is an odd function.

Accepted Answer

The answer of A function has a domain [-4, 4]...

Exam 1: Functions and Models

Determine the number of solutions of the equation 5x $4$ - 3x $2$ = 10x $5$ - 20x $6$ $+$ 63x $+$ 5.

Find the domain of the inverse for f (x) = $\sqrt { 2 x - 5 }$ .

Find functions f and g such that F(x) = 1 $\sqrt { 1 - \cos ^ { 2 } x }$ = $( f \circ g ) ( x )$

Which of the following are graphs of functions?

Make a rough sketch of the graph of y = (1.1) $- x$ . Do not use a calculator.

Relative to the graph of y = sin x, where x is in the radians, the graph of y = sin x, where x is in degrees, is changed in what way?

Make a rough sketch of the graph of y = 3 (4 - 2 $x$ ). Do not use a calculator.

Solve the equation $\log _ { 9 }$ (ln $x ^ { 3 }$ ) = 1

Let f (x) = $\sqrt { 16 - x ^ { 2 } }$ . Find each of the following: (a) f (0) $+$ f ( $- 2$ ) (b) f (x $+$ 2) (c) [f (x)] $2$ (d) f (x $2$ )

Find the smallest value in the domain of the function f (x) = $\sqrt { 2 x - 5 }$ .

Find the range of the function $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } - 4 x & \text { if } x \leq 2 \\| x - 4 | & \text { if } x > 2\end{array} \right.$ .

Find the range of the inverse for f (x) = $- \frac { 3 } { 5 + 2 x }$ .

Find the value of log $2$ $\frac { 1 } { 8 }$ .

Find the inverse function for f (x) = $\frac { x - 1 } { x + 1 }$ .

A function has a domain [-4, 4] and a portion of its graph is shown. (a) Complete the graph of f of its is known that f is an even function.(b) Complete the graph of f if it is known that f is an odd function.

Exam 1: Functions and Models

Determine the number of solutions of the equation 5x 444 - 3x 222 = 10x 555 - 20x 666 +++ 63x +++ 5.

Find the domain of the inverse for f (x) = 2x−5\sqrt { 2 x - 5 }2x−5​ .

Find functions f and g such that F(x) = 1 1−cos⁡2x\sqrt { 1 - \cos ^ { 2 } x }1−cos2x​ = (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Which of the following are graphs of functions?

Make a rough sketch of the graph of y = (1.1) −x- x−x . Do not use a calculator.

Relative to the graph of y = sin x, where x is in the radians, the graph of y = sin x, where x is in degrees, is changed in what way?

Make a rough sketch of the graph of y = 3 (4 - 2 xxx ). Do not use a calculator.

Solve the equation log⁡9\log _ { 9 }log9​ (ln x3x ^ { 3 }x3 ) = 1

Let f (x) = 16−x2\sqrt { 16 - x ^ { 2 } }16−x2​ . Find each of the following: (a) f (0) +++ f ( −2- 2−2 ) (b) f (x +++ 2) (c) [f (x)] 222 (d) f (x 222 )

Find the smallest value in the domain of the function f (x) = 2x−5\sqrt { 2 x - 5 }2x−5​ .

Find the range of the function f(x) ={x2−4x if x≤2∣x−4∣ if x>2f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } - 4 x & \text { if } x \leq 2 \\| x - 4 | & \text { if } x > 2\end{array} \right.f(x) ={x2−4x∣x−4∣​ if x≤2 if x>2​ .

Find the range of the inverse for f (x) = −35+2x- \frac { 3 } { 5 + 2 x }−5+2x3​ .

Find the value of log 222 18\frac { 1 } { 8 }81​ .

Find the inverse function for f (x) = x−1x+1\frac { x - 1 } { x + 1 }x+1x−1​ .

A function has a domain [-4, 4] and a portion of its graph is shown. (a) Complete the graph of f of its is known that f is an even function.(b) Complete the graph of f if it is known that f is an odd function.

Determine the number of solutions of the equation 5x $4$ - 3x $2$ = 10x $5$ - 20x $6$ $+$ 63x $+$ 5.

Find the domain of the inverse for f (x) = $\sqrt { 2 x - 5 }$ .

Find functions f and g such that F(x) = 1 $\sqrt { 1 - \cos ^ { 2 } x }$ = $( f \circ g ) ( x )$

Make a rough sketch of the graph of y = (1.1) $- x$ . Do not use a calculator.

Make a rough sketch of the graph of y = 3 (4 - 2 $x$ ). Do not use a calculator.

Solve the equation $\log _ { 9 }$ (ln $x ^ { 3 }$ ) = 1

Let f (x) = $\sqrt { 16 - x ^ { 2 } }$ . Find each of the following: (a) f (0) $+$ f ( $- 2$ ) (b) f (x $+$ 2) (c) [f (x)] $2$ (d) f (x $2$ )

Find the smallest value in the domain of the function f (x) = $\sqrt { 2 x - 5 }$ .

Find the range of the function $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } - 4 x & \text { if } x \leq 2 \\| x - 4 | & \text { if } x > 2\end{array} \right.$ .

Find the range of the inverse for f (x) = $- \frac { 3 } { 5 + 2 x }$ .

Find the value of log $2$ $\frac { 1 } { 8 }$ .

Find the inverse function for f (x) = $\frac { x - 1 } { x + 1 }$ .